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This is the first semester of a two-semester sequence on Differential Analysis. Topics include fundamental solutions for elliptic, hyperbolic and parabolic differential operators, a method of characteristics. In addition to that review of Lebesgue integration, distributions, Fourier transform, homogeneous distributions and asymptotic methods will also be discussed in this course. If students are interested in this course then this course is the perfect one.
Assessment
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
Certification
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Course Credit: MIT
Course Curriculum
Module: 01 | |||
Continuous Functions | 00:15:00 | ||
Measures and σ-algebras | 00:10:00 | ||
Measureability of Functions | 00:05:00 | ||
Integration | 00:20:00 | ||
Hilbert Space | 00:05:00 | ||
Module: 02 | |||
Test Functions | 00:15:00 | ||
Tempered Distributions | 00:10:00 | ||
Convolution and Density | 00:20:00 | ||
Fourier Inversion | 00:10:00 | ||
Sobolev Embedding | 00:05:00 | ||
Differential Operators | 00:30:00 | ||
Module: 03 | |||
Cone Support and Wavefront Set | 00:20:00 | ||
Homogeneous Distributions | 00:05:00 | ||
Spectral Theorem | 00:05:00 | ||
Problems | 01:00:00 | ||
Solutions | 00:10:00 | ||
References | 00:05:00 | ||
Assessment | |||
Submit Your Assignment | 00:00:00 | ||
Certification | 00:00:00 |
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